What are the best entry level integrated amps and speakers?

Elac is getting so much press for being top performing gear, you must pay that some credence. Perhaps 50% of your budget goes to the speakers.
Right now on audiogon there is a steal on a classe integrated amplifier with a small defect. Original price $2000+, selling for six and change.

There is also an amplifier available now on Audiogon from Peachtree. It is their nova integrated with built-in DAC. I had a peach tree deco for a while, and it was great. The nova is even better! It is selling for 600 something.

add a pair of entry level kimber Or audioquest speaker cables for $150 and you have a fantastic system for $1500!

There’s a Rega Brio R here for $500 and a nice pair of slim tower Silverline Preludes at US Audio Mart for $850 (although you might be able to get this down a bit). The Brio puts out a strong 50W, and the Preludes are a pretty easy load so they should pair well. This still leaves $150 for some decent cables/interconnects. Excellent all-around performance and attractive with a small footprint, which I’d think a girl especially would appreciate. She’ll love it.  Heck, I'd love it!  Best of luck.

Stay away from NAD unless you want to buy a new amp next year. Serious qc issues. It will sound great then let you down. 

RR2160 Stereo Receiver
http://www.outlawaudio.com/products/rr2160.html

"THE OUTLAW AUDIO RR 2160 STEREO RECEIVER FLAT OUT SOUNDS BETTER THAN ANY RECEIVER OR AMPLIFIER I'VE HEARD FOR ITS $799 ASKING PRICE." - Steve Guttenberg, CNET 

"MAKE NO MISTAKE, THE OUTLAW AUDIO RR2160 STEREO RETRO RECEIVER MAY LOOK OLD FASHIONED, BUT IT IS READY FOR THE FUTURE. YOU WILL WANT TO RIDE OFF INTO THE SUNSET WITH THIS OUTLAW!" - Jim Milton, Secrets of Home Theater and Hi-Fidelity 

There's also an almost new Creek Evolution 50a, which would be a very good buy.  Combine with speakers of choice, but I doubt you'd beat the aforementioned Silverlines.